Express this product in scientific notation: $(7.90\times 10^{-1})\times (2.00\times 10^{3})$
Solution: Start by collecting like terms together. $= (7.90\times 2.00) \times (10^{-1}\times 10^{3})$ When multiplying exponents with the same base, add the powers together. $= 15.8 \times 10^{-1\,+\,3}$ $= 15.8 \times 10^{2}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the left without changing the value of our answer. $ $ We can use the fact that $15.8$ is the same as $1.580 \times 10$ $ = {1.580 \times 10} \times 10^{2} $ $= 1.580\times 10^{3}$